Everybody cares what their self-image is and how others view them. The idea of maintaining a "good" self image has been around for so long that the desire have a good image to other people seems completely normal; and to an extent it is: but at what point does it become unhealthy?
It is one thing to be self aware of your actions and words in a social situation to prevent backlash or offending anyone, it is another if everything you do and say is based on what you believe would make other people happy or satisfied.
I see people everyday sacrificing their own happiness and their own mindsets/opinions in order to please those around them, to maintain a good reputation. This makes me extremely sad as what has our society come to that people have to undermine their own self worth in order to feel as if they "fit in" or "have a good reputation."
Some care about their reputations so much that they're constantly thinking about how people view them and what they can do to change the way people view them. Obviously, having that kind of mindset is extremely unhealthy as they're basing their own happiness off of the way they are viewed, which puts them in a completely powerless situation where the only way they can be happy is if someone "lets" them be happy.
Of course it is easy to just simply tell those people to "get over it and start loving yourself for who you are", but it is definitely not that simple with peer pressure and other restrictions society has set on us. The best we can do is to always keep in mind while we are going about our everyday lives that everything we do should be only for us and what makes us happy, everyone else's opinions (for the most part) are and should not matter more than your own.